Finite Group Databasebeta

← #18071331

Subgroups — #18071331

Order 4864.

492 conjugacy classes of subgroups; only the 87 normal subgroups are shown.

normal subgroups only

This group has 492 conjugacy classes of subgroups — too many to draw. Only its 87 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14564963C212yesmaximal, complemented
2#14564717C211yesmaximal, characteristic
3#14561458C212yesmaximal, complemented
4#14561456C211yesmaximal, characteristic
5C19×#2724C211yesmaximal, characteristic
6C22×#64526—21no—
7C2×#10597315C2211yescharacteristic
8C2×#10597264—22no—
9C2×#10597267—21no—
10#11926306—22no—
11#11926299C2212yes—
12#11926299C2211yescharacteristic
13C2×C19×#123—21no—
14C19×#398—21no—
15C19×#397—22no—
16C19×#390C2211yescharacteristic
17C19×#389C2212yes—
18C19×#385—22no—
19C22×D4×C19D411yescharacteristic
20C23×C4×C19—21no—
21C22×Dic38—21no—
22C19×#123—42no—
23C19×#123—42no—
24C2×C4⋊C4×C19—22no—
25C2×C4⋊C4×C19—21no—
26C2×C4⋊C4×C19D412yes—
27C2×C4⋊C4×C19D411yescharacteristic
28C2×C4⋊C4×C19D412yes—
29C2×C22⋊C4×C19—22no—
30C2×C22⋊C4×C19—21no—
31C2×C22⋊C4×C19—22no—
32C2×C42×C19C2311yescharacteristic
33C2×#64526—42no—
34C2×#64526—42no—
35C2×#64526—42no—
36C2×C4⋊Dic19—22no—
37C22×C19⋊C8—21no—
38C22×C19⋊C8—22no—
39#10597315—42no—
40C19×#95—22no—
41C19×#95—21no—
42C19×#95—22no—
43#10597267—42no—
44#10597264—44no—
45C24×C19—21no—
46C2×D4×C19—21no—
47C2×D4×C19—41no—
48C2×D4×C19—41no—
49C2×D4×C19D812yes—
50C22×C4×C19—22no—
51C22×C4×C19—21no—
52C22×C4×C19—22no—
53C22×C4×C19—42no—
54C22×C4×C19—81no—
55C22×C4×C19—81no—
56C22×C4×C19C2×D411yescharacteristic
57C22×C4×C19C2×D412yes—
58C22×Dic19—41no—
59C2×Dic38—22no—
60C2×Dic38—41no—
61C2×Dic38—41no—
62C2×Dic38—41no—
63C2×Dic38—41no—
64C2×Dic38—41no—
65C4⋊C4×C19—22no—
66C4⋊C4×C19—22no—
67C4⋊C4×C19—42no—
68C4⋊C4×C19—41no—
69C4⋊C4×C19—42no—
70C4⋊C4×C19—42no—
71C4⋊C4×C19—81no—
72C22⋊C4×C19—42no—
73C22⋊C4×C19—44no—
74C22⋊C4×C19—42no—
75C22⋊C4×C19—42no—
76C42×C19—41no—
77#64526—48no—
78C4⋊Dic19—24no—
79C4⋊Dic19—42no—
80C2×C19⋊C8—22no—
81C2×C19⋊C8—24no—
82C2×C19⋊C8—41no—
83C2×C19⋊C8—42no—
84C2×C19⋊C8—41no—
85C2×C19⋊C8—42no—
86#7751—191nomaximal, Sylow
87C23×C19—22no—
88C23×C19—42no—
89C23×C19—41no—
90C23×C19—42no—
91C23×C19—41no—
92C23×C19#12011yescharacteristic
93D4×C19—42no—
94D4×C19—81no—
95C2×C4×C19—21no—
96C2×C4×C19—22no—
97C2×C4×C19—22no—
98C2×C4×C19—21no—
99C2×C4×C19—42no—
100C2×C4×C19—42no—
101C2×C4×C19—42no—
102C2×C4×C19—42no—
103C2×C4×C19—41no—
104C2×C4×C19—42no—
105C2×C4×C19—42no—
106C2×C4×C19—42no—
107C2×C4×C19—84no—
108C2×C4×C19C2×D811yescharacteristic
109C2×C4×C19#13512yes—
110C2×C4×C19AGL(1,ℤ/8)11yescharacteristic
111C2×C4×C19#13712yes—
112C2×Dic19—42no—
113C2×Dic19—81no—
114C2×Dic19—81no—
115Dic38—42no—
116Dic38—42no—
117Dic38—81no—
118Dic38—81no—
119C19⋊C8—44no—
120C19⋊C8—42no—
121#2724D1911yescharacteristic
122#2057—192no—
123#2013—191no—
124#1271—192no—
125#1270—191no—
126C22×C19—42no—
127C22×C19—44no—
128C22×C19—82no—
129C22×C19—81no—
130C22×C19—81no—
131C22×C19#44711yescharacteristic
132C22×C19#45212yes—
133C22×C19#45311yescharacteristic
134C22×C19#45612yes—
135C22×C19B(4,𝔽2)11yescharacteristic
136C4×C19—21no—
137C4×C19—21no—
138C4×C19—22no—
139C4×C19—22no—
140C4×C19—82no—
141C4×C19—81no—
142C4×C19—82no—
143Dic19—82no—
144C22×SD16—381no—
145C2×C4⋊Q8—191no—
146C2×#123—21no—
147C2×#107—382no—
148C2×#103—381no—
149#398—21no—
150#397—22no—
151#390C2×D1911yescharacteristic
152#389C2×D1912yes—
153#385—22no—
154#340—382no—
155#336—192no—
156#336—191no—
157C2×C19—82no—
158C2×C19#159511yescharacteristic
159C2×C19#160312yes—
160C2×C19#163011yescharacteristic
161C2×C19#164712yes—
162C2×C19#166011yescharacteristic
163C22×Q8—381no—
164C22×D4C22⋊D1911yescharacteristic
165C23×C4—21no—
166C2×SD16—762no—
167C2×SD16—762no—
168C2×SD16—762no—
169C22×C8—381no—
170C22×C8—382no—
171C4⋊Q8—762no—
172#123—42no—
173#123—42no—
174C2×C4⋊C4—22no—
175C2×C4⋊C4—21no—
176C2×C4⋊C4—382no—
177C2×C4⋊C4C22⋊D1912yes—
178C2×C4⋊C4C22⋊D1912yes—
179C2×C4⋊C4C22⋊D1911yescharacteristic
180C2×C22⋊C4—22no—
181C2×C22⋊C4—21no—
182C2×C22⋊C4—22no—
183C2×C42C22×D1911yescharacteristic
184#107—764no—
185#103—762no—
186#95—22no—
187#95—21no—
188#95—22no—
189C19#775111yescharacteristic, complemented, Sylow
190C24—21no—
191C2×Q8—382no—
192C2×Q8—761no—
193C2×Q8—761no—
194C2×Q8—761no—
195C2×Q8—761no—
196C2×Q8—761no—
197C2×D4—21no—
198C2×D4—41no—
199C2×D4—41no—
200C2×D4#6452512yes—
201C22×C4—22no—
202C22×C4—21no—
203C22×C4—22no—
204C22×C4—42no—
205C22×C4—81no—
206C22×C4—81no—
207C22×C4—761no—
208C22×C4C2×C22⋊D1911yescharacteristic
209C22×C4C2×C22⋊D1912yes—
210SD16—768no—
211C2×C8—382no—
212C2×C8—384no—
213C2×C8—762no—
214C2×C8—761no—
215C2×C8—761no—
216C2×C8—762no—
217C4⋊C4—22no—
218C4⋊C4—22no—
219C4⋊C4—41no—
220C4⋊C4—42no—
221C4⋊C4—42no—
222C4⋊C4—42no—
223C4⋊C4—81no—
224C4⋊C4—384no—
225C4⋊C4—762no—
226C22⋊C4—42no—
227C22⋊C4—44no—
228C22⋊C4—42no—
229C22⋊C4—42no—
230C42—41no—
231C23—22no—
232C23—42no—
233C23—41no—
234C23—42no—
235C23—41no—
236C23#1059739911yescharacteristic
237Q8—762no—
238Q8—762no—
239Q8—1521no—
240Q8—1521no—
241D4—42no—
242D4—81no—
243C2×C4—21no—
244C2×C4—22no—
245C2×C4—22no—
246C2×C4—21no—
247C2×C4—42no—
248C2×C4—42no—
249C2×C4—42no—
250C2×C4—42no—
251C2×C4—41no—
252C2×C4—42no—
253C2×C4—42no—
254C2×C4—42no—
255C2×C4—84no—
256C2×C4—762no—
257C2×C4—1521no—
258C2×C4—1521no—
259C2×C4C2×#6452511yescharacteristic
260C2×C4#1059737811yescharacteristic
261C2×C4#1059739612yes—
262C2×C4#1059739712yes—
263C8—762no—
264C8—764no—
265C22—44no—
266C22—42no—
267C22—82no—
268C22—81no—
269C22—81no—
270C22#1192667811yescharacteristic
271C22#1192670612yes—
272C22#1192671211yescharacteristic
273C22#1192672712yes—
274C22#1192673111yescharacteristic
275C4—22no—
276C4—22no—
277C4—21no—
278C4—21no—
279C4—82no—
280C4—81no—
281C4—82no—
282C4—1522no—
283C2—82no—
284C2#1456255311yescharacteristic
285C2#1456259812yes—
286C2#1456275611yescharacteristic
287C2#1456287012yes—
288C2#1456294611yescharacteristic
subgroupG/H
centerC23#10597399
commutator, cosocleC2×C42×C19C23
FrattiniC2×C42C22×D19
FittingC19×#2724C2
socleC23×C19#120
prime radicalC22×D4×C19D4
hypercenter#2724D19
hypocenterC19#7751
LCSG ▷ C2×C42×C19 ▷ C23×C19 ▷ C19
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2724

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. #14564963C2semidirect
3. #14561458C2semidirect
189. C19#7751semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#145649632
#145647172
#145614582
#145614562
C19×#27242
#775119